[论文解读] MPM Lite: Linear Kernels and Integration without Particles

Xiang Feng, Yunuo Chen+7 more|arXiv (Cornell University)|Feb 8, 2026

Computer Graphics and Visualization Techniques被引用 0

一句话总结

MPM Lite 提出了一种混合拉格朗日/欧拉方法，通过将粒子数据重新采样到固定网格求积点，消除了求解时的基于粒子的求积，从而实现类似 FEM 的隐/显式求解，与粒子无关。

ABSTRACT

In this paper, we introduce MPM Lite, a new hybrid Lagrangian/Eulerian method that eliminates the need for particle-based quadrature at solve time. Standard MPM practices suffer from a performance bottleneck where expensive implicit solves are proportional to particle-per-cell (PPC) counts due to the the choices of particle-based quadrature and wide-stencil kernels. In contrast, MPM Lite treats particles primarily as carriers of kinematic state and material history. By conceptualizing the background Cartesian grid as a voxel hexahedral mesh, we resample particle states onto fixed-location quadrature points using efficient, compact linear kernels. This architectural shift allows force assembly and the entire time-integration process to proceed without accessing particles, making the solver complexity no longer relate to particles. At the core of our method is a novel stress transfer and stretch reconstruction strategy. To avoid non-physical averaging of deformation gradients, we resample the extensive Kirchhoff stress and derive a rotation-free deformation reference solution, which naturally supports an optimization-based incremental potential formulation. Consequently, MPM Lite can be implemented as modular resampling units coupled with an FEM-style integration module, enabling the direct use of off-the-shelf nonlinear solvers, preconditioners, and unambiguous boundary conditions. We demonstrate through extensive experiments that MPM Lite preserves the robustness and versatility of traditional MPM across diverse materials while delivering significant speedups in implicit settings and improving explicit settings at the same time. Check our project page at https://mpmlite.github.io.

研究动机与目标

• Motivate and develop a particle-quadrature-free solver to remove PPC-dependent bottlenecks in MPM.
• Maintain robustness and versatility across elastoplastic materials while using fixed-grid FEM-like integration.
• Enable straightforward integration with off-the-shelf nonlinear solvers and boundary condition handling.

提出的方法

• Treat the Cartesian grid as a voxel hexahedral mesh and resample particle fields to fixed-location quadrature points using compact linear kernels.
• Perform force assembly and time integration entirely on the grid, with particles used only for advection and constitutive updates.
• Transfer momentum and stress via a linear-kernel, second-order consistent velocity transfer and a rotation-free stretch-based stress reconstruction.
• Adopt an incremental potential formulation with a rotation-free base stretch to enable objective, grid-based implicit solves.
• Reconstruct stress and stretch through Kirchhoff stress aggregation on centers, followed by FEM-like integration on the grid.
• Support multiple materials by keeping per-material quadrature at centers and aggregating energy contributions in an updated-Lagrangian framework.

实验结果

研究问题

• RQ1 Can solver complexity be decoupled from particle-per-cell counts by moving integration away from particles?
• RQ2 Does the rotation-free stretch reconstruction yield objective, stable implicit updates for isotropic materials?
• RQ3 How do linear-kernel transfers compare to APIC/B-spline schemes in accuracy and stability while enabling FEM-like solvers?
• RQ4 What performance gains (explicit and implicit) can be achieved over traditional MPM variants while preserving material versatility?

主要发现

• MPM Lite achieves 1.88× speedup over explicit MPM and 15.9× speedup over implicit MPM in practical elastoplastic materials.
• The approach preserves robustness and versatility of traditional MPM across diverse materials while reducing solver cost, particularly for implicit settings.
• A rotation-free stretch reference solution enables an optimization-based incremental formulation compatible with standard nonlinear solvers and boundary conditions.
• Linear-kernel transfers provide second-order consistency with APIC while maintaining compact stencils and grid-centric force assembly.